On some properties of finite sums of ridge functions defined on convex subsets of \(\mathbb{R}^n\)

DOI10.1134/S0081543816040131zbMath1370.26028OpenAlexW2479596153MaRDI QIDQ338497

A. A. Kuleshov, Sergei V. Konyagin

Publication date: 7 November 2016

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543816040131

zbMATH Keywords

continuityrate of growthridge function

Mathematics Subject Classification ID

Continuity and differentiation questions (26B05) Rate of growth of functions, orders of infinity, slowly varying functions (26A12) Representation and superposition of functions (26B40)

Related Items (7)

A note on the equioscillation theorem for best ridge function approximation ⋮ Continuous sums of ridge functions on a convex body and the class VMO ⋮ On some properties of smooth sums of ridge functions ⋮ Some problems in the theory of ridge functions ⋮ A note on continuous sums of ridge functions ⋮ On the representation by bivariate ridge functions ⋮ A representation problem for smooth sums of ridge functions

Cites Work

• Entropy numbers of embedding operators for weighted Sobolev spaces
• Interpolation on lines by ridge functions
• On functions with bounded \(n\)-th differences
• On the continuity of finite sums of ridge functions
• On a smoothness problem in ridge function representation
• Additive and multiplicative anisotropic estimates for integral norms of differentiable functions on irregular domains
• The fundamentality of sets of ridge functions
• Optimal reconstruction of a function from its projections
• On best approximation by ridge functions
• The Whitney constants are bounded by two
• Interpolation by Ridge functions
• Widths of Sobolev weight classes on a domain with cusp
• Ridge Functions
• Best approximation of functions of two variables by functions of the form 𝜑(𝑥)+𝜓(𝑦)
• Axiom of choice
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